External Harmonic Signal Research Articles

Giant injection-locking bandwidth of a self-pulsing limit-cycle in an optomechanical cavity

Locking of oscillators to ultra-stable external sources is of paramount importance for improving close-to-carrier phase noise in free running oscillators. In most of them, such as Micro-Electro-Mechanical-Systems or LC circuit-based oscillators, the locking frequency range is limited by the robustness of their natural frequency, which comes explicitly related with intrinsic parameters of the system. In this work we report the synchronization of an optically-driven self-pulsing limit-cycle taking place in a silicon optomechanical crystal cavity to an external harmonic signal that modulates the driving laser. Because of the extreme ductility of the natural self-pulsing frequency (several tens of MHz), the injection-locking mechanism is highly efficient and displays giant relative bandwidths exceeding 60%. The external modulation reveals itself as a knob to explore dynamical attractors that are otherwise elusive and, in particular, as a means to initialize a mechanical resonator into a state of self-sustained oscillations driven by radiation pressure forces. Moreover, we exploit the large anharmonicity of the studied limit-cycle to induce injection-locking to integer multiples and fractions of the frequency of the external reference, which can be used for frequency conversion purposes in nano-electro-opto-mechanical systems.

Creating electronic oscillator-based Ising machines without external injection locking

Coupled electronic oscillators have recently been explored as a compact, integrated circuit- and room temperature operation-compatible hardware platform to design Ising machines. However, such implementations presently require the injection of an externally generated second-harmonic signal to impose the phase bipartition among the oscillators. In this work, we experimentally demonstrate a new electronic autaptic oscillator (EAO) that uses engineered feedback to eliminate the need for the generation and injection of the external second harmonic signal to minimize the Ising Hamiltonian. Unlike conventional relaxation oscillators that typically decay with a single time constant, the feedback in the EAO is engineered to generate two decay time constants which effectively helps generate the second harmonic signal internally. Using this oscillator design, we show experimentally, that a system of capacitively coupled EAOs exhibits the desired bipartition in the oscillator phases without the need for any external second harmonic injection, and subsequently, demonstrate its application in solving the computationally hard Maximum Cut (MaxCut) problem. Our work not only establishes a new oscillator design aligned to the needs of the oscillator Ising machine but also advances the efforts to creating application specific analog computing platforms.

Study of gyrotron synchronization by an external harmonic signal based on a modified quasi-linear theory

Topic. The paper is devoted to the study of synchronization of a gyrotron by an external harmonic signal. A theoretical study of gyrotron synchronization processes by means of a computational experiment based on certain traditional models of microwave electronics does not provide a complete description of the synchronization pattern. Therefore, the goal of the paper is to develop a modified quasi-linear model based on an approximation of the electron susceptibility by rational functions. Methods. The developed model allows for bifurcation analysis of synchronization processes. On its basis, stationary states are determined and their stability analysis is carried out. The results are in good agreement with numerical simulation based on the non-stationary theory of a gyrotron with a fixed Gaussian high-frequency field structure. Results and discussion. Resonance curves and synchronization bounds are built on the plane of parameters “amplitude – frequency of external signal”. The case where the gyrotron is in the hard excitation mode is considered, since the maximum efficiency is usually achieved in the hard excitation mode. In general, the results are in qualitative agreement with the picture described earlier for a simpler quasi-linear model of a oscillator with hard excitation, in the case of a sufficiently strong phase nonlinearity.

The dynamics of synchronization of two-stage van der Pol generator

Results of numerical simulation of self-oscillations synchronization process in two-cascade ring generator van der Pol by harmonic signal are presented. Studies were carried out within the framework of the DT- model of the dynamic system. The model was developed on the basis of the principle of compliance within the framework of the method of slowly changing amplitudes of characteristics of a discrete system with characteristics of an analog prototype. Shortened equations for complex oscillation amplitudes in generator stages are obtained. It was found that in an autonomous system there is an effect of bistability of amplitudes. In the synchronization mode with an external harmonic signal, solutions of shortened equations made it possible to calculate amplitude-frequency and phase-frequency characteristics of synchronous oscillations. It is shown that transitions between bistable states are observed in the synchronous oscillation holding band. Differences of frequency characteristics of synchronization of classical and two-stage oscillators van der Pol were analyzed.

Laminar Chaos in a Delayed-Feedback Generator

The phenomenon of laminar chaos is experimentally investigated for the first time in a radioengineering delayed-feedback generator in which the delay time is modulated by an external harmonic signal. The regions of existence of various regimes of laminar chaos on the plane of parameters of external excitation are plotted. The nonlinear function of the generator in the laminar chaotic regime is reconstructed.

Ламинарный хаос в генераторе с запаздывающей обратной связью

For the first time, the phenomenon of laminar chaos is experimentally studied in a radio engineering generator with time-delayed feedback, the delay time of which is modulated by an external harmonic signal. Regions of various regimes of laminar chaos are constructed on the plane of the parameters of modulating signal. The nonlinear function of generator is reconstructed in the regime of laminar chaos.

Robust guaranteed performance PID controller design for non-minimum phase plants

Abstract The paper presents a new original robust PID design method for non-minimum phase plants to achieve closed-loop performance prescribed by the process technologist in terms of settling time and maximum overshoot, respectively. The proposed design procedure has two steps: first, the uncertain system is identified using external harmonic excitation signal with frequency, second, the controller of the nominal system is designed for specified gain margin. A couple of parameters is obtained from the time domain performance specification using quadratic regression curves, the so-called performance Bparabolas so, as to simultaneously satisfy robust closed-loop stability conditions. The main benefits of the proposed method are universal applicability for systems with both fast and slow dominant dynamics as well as performance specification using time domain criteria. The proposed PID design method has been verified on a set of benchmark systems.

The possibility of amplification and generation of higher harmonics in a microwave device with turbulent electron flow (Natural experiment and phenomenological model)

A generator of turbulent electron beams in an independent mode and in the mode of amplification of an external single-frequency signal is experimentally investigated. The formation of higher harmonic components in the spectrum of output radiation of the generator is shown experimentally. The phenomenological model of the turbulent electron flow is constructed on the basis of a chain of interacting “electron vortices” described by the modified nonlinear Van-der-Pol differential equations. The modes of independent dynamics and the mode of amplification of an external harmonic signal are considered. The results of numerical modeling and experimental investigations are compared. The qualitative correspondence of the behavior of the dependences obtained from the experimental investigation of the generator of turbulent electron beams and the results obtained from numerical modeling is shown.

High-frequency impedance of semiconductor superlattice elements in external resonance system

We have studied the high-frequency (HF) impedance of a semiconductor superlattice coupled to an external electrodynamic system, which is a promising element of devices for terahertz (THz) and sub-THz frequency ranges. A characteristic behavior of the impedance under the action of an external harmonic HF signal in the region of synchronization at the fundamental and high-order resonance frequencies of the domain transport system is determined. It is shown that the diagnostics of synchronous regimes in a semiconductor superlattice in an external resonator can be based on analysis of the dynamics of amplitude and phase of the HF impedance.

Effect of the electron beam modulation on the sub-THz generation in the vircator with the field-emission cathode

In this paper, we focus on the numerical investigation of the vircator with a controlling emission from a field-emission cathode. The external harmonic signal is added to the accelerating electric field in the beam formation region and effects on the beam emission process leading to the electron emission modulation. As a consequence, the beam is injected into the drift chamber of the vircator being density-modulated. The strong influence of the modulation parameters (modulation depth and frequency) on the characteristics of virtual cathode oscillations has been discovered. We have shown that the tuning of the modulation frequency to the harmonics of the basic frequency of virtual cathode oscillations leads to the considerable power increase of its higher harmonics in the output spectrum.

The effect of an external signal on output microwave power of a low-voltage vircator

Abstract This Letter is devoted to results of the both experimental and theoretical studies of electromagnetic radiation output power gain in the low-voltage microwave generator with a virtual cathode (vircator) under an external harmonic signal leading to the preliminary velocity modulation of the electron beam. The simple theoretical model of the electron beam with virtual cathode in a diode gap with retarding field under the external signal has been developed. The theoretical and numerical analysis have shown the possibility of power amplification in the vircator under the external influence. Obtained results of the theoretical consideration are proven by the experimental study.

The mean Poincaré return time locking: A criterion of chaos induced synchronization

A new method for diagnostics of the induced synchronization of chaotic self-oscillation is proposed, which is based on the local theory of Poincare recurrences. It is established that, in the region of synchronization, the mean Poincare return time is locked by an external harmonic signal.

Stochastic resonance of vortices in a washboard pinning potential

In a bistable potential at low temperatures, stochastic resonance can be characterized as a synchronization effect of the hopping mechanism induced by an external periodic stimulus, where synchronization attains a maximum by fine-tuning the forcing frequency close to the relevant switching rate. In this work, we theoretically investigate the nonlinear single-vortex dynamics in a tilted cosine (multistable) washboard pinning potential at nonzero temperature in the presence of dc and ac currents of arbitrary amplitudes and frequency. The conditions for stochastic resonance to appear are derived on the basis of the exact solution of the corresponding Langevin equation for non-interacting vortices in terms of a matrix continued fraction. The nonlinear ac voltage response is analyzed as a function of temperature, dc bias, ac amplitude and frequency, with particular focus on the amplification of the external harmonic signal and its conversion to the third harmonics of the input frequency.

Intermittent behavior near the synchronization threshold in system with fluctuating control parameter

In this paper the characteristics of the intermittent behavior observed near the synchronization threshold of a periodic oscillator driven by the external harmonic signal are studied in the case when the amplitude of the external signal fluctuates, i.e., it changes its value randomly in some moments of time. The analytical law for the distribution of the laminar phases lengths has been deduced. The very good agreement between the discovered theoretical law and the results of numerical simulation has been shown.

Theoretical and experimental analysis of the microwave radiation power of a generator on a virtual cathode subjected to external harmonic exposure

Analytical, numerical, and experimental investigations of the output power of a generator are performed on a virtual cathode under the effect of an external harmonic signal. It is shown theoretically that an increase in the power of the external effect leads to an increase in the output power of a nonautonomous oscillator. The results from our theoretical analysis are in good agreement with the results from a pilot study.

Effect of external signal on the output power of an oscillator with electron feedback

The effect of an external single-frequency harmonic signal on the output power of an oscillator with electron feedback has been studied by analytical and numerical methods. It is established that an increase in the input signal power leads to sharp growth in the output power of the nonautonomous oscillator. Physical processes that take place in the electron beam with virtual cathode under the action of an external harmonic signal, which leads to velocity modulation in the electron beam entering the interaction space, have been analyzed. The obtained results well agree with the data of previous experimental investigations of the signal gain in a low-voltage vircator.

SYNCHRONIZATION OF FRACTIONAL VAN-DER-POL OSCILLATOR

A model of self-oscillating system with a differential equation of motion of fractional order under the action of external harmonic signal is proposed. Solutions of equation of motion which correspond to the regime of steady-state synchronized oscillations and the regime of beats near the synchronization band are obtained in the quasiharmonic approximation. The amplitude frequency and phase-frequency characteristics of synchronization of fractional Van-der-Pol oscillator are analyzed. An analogy between the generator with a fractional feedback circuit and the generator with delayed feedback is established.

Features of induced synchronization of a bistable oscillator with chaotic dynamics

The features of induced synchronization of a Chua oscillator with a nonlinear element admitting cubic approximation have been numerically simulated for a system where the autonomous operation admits regular or chaotic regimes determined by losses in the oscillatory circuit. The cases of deterministic synchronization (under the action of a harmonic external driving signal) and chaotic synchronization (chaotic control) have been considered. It is established that, outside the band of synchronous oscillations that corresponds to the deterministic synchronization, the external harmonic signal stimulates the transformation of regular oscillations into chaos with the motions switched between two attractors. In cases of chaotic synchronization, there is a residual “noise” in the form of differential chaotic oscillations, which grows with increasing non-identity of the driving and driven signals.

Coherent resonance in klystron oscillator at self-excitation threshold

The phenomenon of coherent resonance in a nonlinear dynamical system based on a delayed-feedback klystron (DFK) oscillator has been experimentally studied. The application of an external white noise signal to the DFK oscillator at the self-excitation threshold leads to the appearance of a resonant response in the system, the maximum of which is attained at a definite power of the external noise. It is demonstrated for the first time that the coherent resonance in response to an external harmonic signal in the microwave range allows the signal-to-noise ratio at the output of a regenerative ring amplifier to be significantly increased.

Forced synchronization of a delayed-feedback oscillator

Dynamics of a delayed-feedback oscillator with cubic nonlinearity driven by an external harmonic signal is considered. Regimes of forced synchronization and their stability conditions are studied analytically and numerically for the cases of single-frequency and multiple-frequency (self-modulation) operation of the free-running oscillator. Special attention is paid to synchronization of the oscillator with bistability of steady states which arises near the boundary of generation zone. Results of numerical simulation of bifurcation transitions to synchronization regime for different driving frequencies are presented. Main differences from the classical picture of synchronization for a system with one degree of freedom are discussed.